Adding on to what John M. shared, if you have a strong female type lead actress you want to feature, and you want to produce Shakespeare, I'd encourage you to look at some other options instead. (Kate actually isn't on stage that much in Shrew; the majority of the time it's the men.)
Much Ado About Nothing and Twelfth Night both feature strong female leads, plus other great female characters, and if there are mysoginistic issues that arise (Much Ado), they are handled well with the male character being "called out" and having to admit his wrongdoing (Claudio).
Especially after #MeToo, Shrew is being produced less, because it is extremely difficult to edit and produce that play while trying to get rid of the multiple issues it has, while maintaining the story and the text.